Which of the following is equal to 2^k*5^(k-1)?
A. 2*10^(k-1)
B. 5*10^(k-1)
C. 10^k
D. 2*10^k )
E. 10^(2k-1)
I'm confused how to set up the formulas here. Can any experts help?
Which of the following is equal to (2^k)(5^k − 1)?
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- ahmedshafea
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There's a nice rule that says (x^k)(y^k) = (xy)^kahmedshafea wrote:Which of the following is equal to 2^k*5^(k-1)?
A. 2*10^(k-1)
B. 5*10^(k-1)
C. 10^k
D. 2*10^k )
E. 10^(2k-1)
For example, (7^11)(10^11) = 70^11
Now recognize that 2^k = 2^1 * 2^(k-1)
So, we get....
2^k * 5^(k-1) = 2^1 * 2^(k-1) * 5^(k-1)
= 2^1 * 2^(k-1) * 5^(k-1)
= 2^1 * 10^(k-1)
Answer: A
Cheers,
Brent
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Hi ahmedshafea,
This question can be solved by TESTing VALUES.
IF... K = 1, then (2^K)(5^[K-1]) =
(2^1)(5^0) =
(2)(1) =
2
So we're looking for an answer that equals 2 when you plug in K = 1. There's only one answer that matches.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This question can be solved by TESTing VALUES.
IF... K = 1, then (2^K)(5^[K-1]) =
(2^1)(5^0) =
(2)(1) =
2
So we're looking for an answer that equals 2 when you plug in K = 1. There's only one answer that matches.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7222
- Joined: Sat Apr 25, 2015 10:56 am
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Let's simplify the given expression:ahmedshafea wrote:Which of the following is equal to 2^k*5^(k-1)?
A. 2*10^(k-1)
B. 5*10^(k-1)
C. 10^k
D. 2*10^k )
E. 10^(2k-1)
2^k * 5^(k-1) = 2^1 * 2^(k-1) * 5^(k-1) = 2 * (2*5)^(k-1) = 2 * 10^(k-1)
Answer: A
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